调制自旋链中的慢扩散与 Thouless 局域化判据
Slow diffusion and Thouless localization criterion in modulated spin chains
AI总结：
本文建立扩散常数与能级结构的关系并导出 Thouless 局域化判据，解释非遍历转变点随系统尺寸近线性漂移，并证明准周期场下海森堡自旋链可由简单周期系统逼近且扩散保持有限。
摘要：
近年来，无序自旋链的遍历性已通过能级统计或输运性质的大规模数值研究得到考察。然而，这些结果之间的明确关系尚未建立。我们给出了扩散常数与能级结构之间的关系，由此导出 Thouless 局域化判据。结合扩散常数对准周期或随机场强度的类指数依赖，Thouless 判据解释了向非遍历态转变的交叉/相变点随系统尺寸几乎线性漂移的现象。此外，我们证明，在存在准周期场的情况下，海森堡自旋链可以通过一系列简单周期系统很好地逼近，在这些周期系统中，即使在大场下扩散仍然保持有限。
英文摘要：
In recent years the ergodicity of disordered spin chains has been investigated via extensive numerical studies of the level statistics or the transport properties. However, a clear relationship between these results has yet to be established. We present the relation between the diffusion constant and the energy-level structure, which leads to the Thouless localization criterion. Together with the exponential-like dependence of the diffusion constant on the strength of quasiperiodic or random fields, the Thouless criterion explains the nearly linear drift with the system size of the crossover/transition to the nonergodic regime. Moreover, we show that the Heisenberg spin chain in the presence of the quasiperiodic fields can be well approached via a sequence of simple periodic systems, where diffusion remains finite even at large fields.
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